We introduce Longitudinal Factor Analysis (LFA) to extract the Common Risk Free (CRF) rate from a sample of sovereign bonds of countries in a monetary union. Since LFA exploits the typically very large longitudinal dimension of bond data, it performs better than traditional factor analysis methods that rely on the much smaller cross-sectional dimension. European sovereign bond yields for the period 2006-2010 are decomposed into a CRF rate, a default risk premium, and a liquidity risk premium, shedding new light on issues such as benchmark status, flight-to-quality and flight-to-liquidity hypotheses. Our empirical findings suggest that investors chase both credit quality and liquidity, and that liquidity is more valued when aggregate risk is high.